Abstract
In this paper, we study algebras of Cartan type *, over a field F of characteristic 0, which is a class of infinite dimensional Lie algebras. These algebras are sets of sums of the images of D h ij where D h ij (f) = h{∂ j (f)∂ i − ∂ i (f)∂ j } for all f and h in the field F(x 1, …, x n ), and occur as subalgebras of the Lie algebra of derivations of the field of rational fuctions. We find the unique minimal ideal of algebras of Cartan type *. We also investigate the size of the ideal for some special cases.
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